VakhitovKolokolov and energy vanishing conditions for linear instability of solitary waves in models of classical self-interacting spinor fields
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We study the linear stability of localized modes in self-interacting spinor fields, analyzing the spectrum of the operator corresponding to linearization at solitary waves. Following the generalization of the Vakhitov--Kolokolov approach, we show that the bifurcation of real eigenvalues from the origin is completely characterized by the Vakhitov--Kolokolov condition $dQ/domega=0$ and by the vanishing of the energy functional. We give the numerical data on the linear stability in the generalized Gross--Neveu model and the generalized massive Thirring model in the charge-subcritical, critical, and supercritical cases, showing the agreement with the Vakhitov--Kolokolov and the energy vanishing conditions.
author list (cited authors)
Berkolaiko, G., Comech, A., & Sukhtayev, A.
complete list of authors
Berkolaiko, Gregory||Comech, Andrew||Sukhtayev, Alim